Equation editor

ABSTRACT

An on-line teaching and learning system with rapid change-by-change or real time reinforcement signals for students and simultaneous monitoring by the teacher of the actual responses as well as their correctness is disclosed. The system may include at least one teacher computer, a plurality of student computers operably connected to the at least one teacher computer by a communications network. The system may be used in a classroom setting or in a distance-learning environment.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional ApplicationNo. 60/445,823, filed on Feb. 10, 2003, entitled “EQUATION EDITOR.” Thisapplication is a divisional application of U.S. Ser. No. 10/775,301,filed on Feb. 10, 2004, entitled “EQUATION EDITOR.”, and published onAug. 12, 2004 as USPA 2004/0157203A1, which is hereby incorporated byreference in its entirety.

U.S. Pat. No. 6,302,698, filed on Feb. 16, 1999, and U.S. ApplicationSerial No. 2001/0034016, filed on Jan. 12, 2001, are hereby incorporatedby reference in their entireties.

FIELD OF THE INVENTION

The present invention generally relates to the field of electronicediting and review. The present invention particularly relates tomethods and systems for creating, editing, transmitting and receivingequations in an electronic format. In a preferred embodiment, one ormore computer systems are used to construct, edit and/or transmitequations to a remote terminal where the submitted equations, forexample, may be reviewed for correctness.

BACKGROUND OF THE INVENTION

Instructors and testing professionals generally regard mathematicalproblem solving experience as an effective method of developing mathskills. In this regard, literature pertaining to the teaching of mathsuggests that solving a greater number of problems may facilitateimprovement in a student's math ability.

As the use of computers in classrooms and in home learning environmentshas increased, students have increasingly desired to solve math problemsusing computer systems. A number of conventional computer-based equationand expression editors have become available for students to use,including MathML, WebMathematica, Quickmath, NetTutor™, and LaTeX.

MathML is intended to facilitate the use and re-use of mathematical andscientific content on the Internet and for other applications such ascomputer algebra systems, print typesetting and voice synthesis. MathMLcan be used to encode both the presentation of mathematical notation forhigh-quality visual displays and mathematical content for applicationswhere semantics are generally important, such as in scientific or voicesynthesis software.

WebMathematica is based on Mathematica Server Page (“MSP”) technology.MSP technology allows a website to include HTML pages that are enhancedby the addition of Mathematica commands. When a user requests such apage, which are generally called MSP scripts or more simply MSPs,Mathematica commands within the page description are evaluated, and theresult is placed on the page.

QuickMath is an automated service for answering common math problemsover the Internet.

LaTeX is a document preparation system that permits high-qualitytypesetting. LaTeX is typically used for medium to large technical orscientific documents; however, it may be used for almost any form ofpublishing.

All of the above-described math tools permit the user to draft equationsusing a computer-based system. However, none of the tools permitsequations to be drafted in a real time teaching environment in whichstudents interact with a teacher.

NetTutor™ is a distance-learning environment for the dissemination ofonline content. NetTutor™ is an Internet-based graphical chat windowthat is threaded and platform independent. It allows students to usetheir computers to access learning materials in a non-linear fashion orin real time with live corresponding tutors. Only one student mayinteract with a tutor at a time although a plurality of students mayview the interaction.

However, NetTutor™ does not permit a teacher to interact with aplurality of students concurrently by posing a question and receivingmathematical expressions as responses from each student. Moreover,mathematical expressions entered into NetTutor™ are not evaluated forcorrectness by the system based on a previously constructed answer set.

What is needed is a system and method for permitting a plurality ofstudents to interact with a teacher using a computer-based equationeditor.

A need exists for a system and method for permitting a plurality ofremote computer systems to receive, edit and submit equations to acentral computer terminal for scoring and/or review.

A further need exists for real time systems and methods for performingone or more of the listed functions.

A still further need exists for a system that can automatically comparereceived responses to a previously constructed answer set for real timedetermination of whether the responses are correct.

The present invention is directed towards solving one or more of theseproblems.

SUMMARY OF PREFERRED EMBODIMENTS

Before the present methods, systems, and materials are described, it isto be understood that this invention is not limited to the particularmethodologies, systems and materials described, as these may vary. It isalso to be understood that the terminology used in the description isfor the purpose of describing the particular versions or embodimentsonly, and is not intended to limit the scope of the present inventionwhich will be limited only by the appended claims.

It must also be noted that as used herein and in the appended claims,the singular forms “a,” “an,” and “the” include plural references unlessthe context clearly dictates otherwise. Thus, for example, reference toan “equation” is a reference to one or more equations and equivalentsthereof known to those skilled in the art, and so forth. Unless definedotherwise, all technical and scientific terms used herein have the samemeanings as commonly understood by one of ordinary skill in the art.Although any methods, materials, and devices similar or equivalent tothose described herein can be used in the practice or testing ofembodiments of the present invention, the preferred methods, materials,and devices are now described. All publications mentioned herein areincorporated by reference. Nothing herein is to be construed as anadmission that the invention is not entitled to antedate such disclosureby virtue of prior invention.

In a preferred embodiment, a system for editing, comparing, andresolving equations includes a communications network, at least oneteacher computer, and a plurality of student computers. Each studentcomputer and each teacher computer are operably connected via thecommunications network. Each teacher computer includes an input device,a display, and a computer-readable storage medium containing programinstructions for implementing a teacher equation editor application.Each student computer includes an input device, a display, and acomputer-readable storage medium containing program instructions forimplementing a student equation editor application.

The teacher equation editor application may include one or more programinstructions for implementing a communications protocol that controlscommunication between the teacher computer and the plurality of studentcomputers via the communications network. The teacher equation editorapplication may include one or more program instructions for receiving aquestion description via the input device, storing the questiondescription, receiving one or more answers corresponding to the questiondescription via the input device, and storing the one or more answers.Each answer may include one or more of an equation and an expression.The input device for the teacher computer may include a pointing deviceand/or a keyboard. In an embodiment, the question description is storedin the computer-readable storage medium of the teacher computer. In anembodiment, one or more answers are stored in the computer-readablestorage medium of the teacher computer. The teacher equation editorapplication further includes one or more program instructions fortransmitting the question description to each student computer via thecommunications network. The teacher equation editor application furtherincludes one or more program instructions for receiving a response fromone of the plurality of student computers via the communicationsnetwork, and comparing the response with the one or more answerscorresponding to the question description. At least one response may bereceived in a rendered format and/or a character syntax. In anembodiment, comparing the response includes rendering the response fromthe character syntax into a rendered expression. The teacher equationeditor application further includes one or more program instructions fordisplaying the rendered expression on the display of the teachercomputer. The teacher equation editor application further includes oneor more program instructions for storing an indication that the responseis correct, if the response is equal to at least one answer, and storingan indication that the response is incorrect, if the response is notequal to at least one answer. The teacher equation editor applicationfurther includes one or more program instructions for generating alearning reinforcement signal. The teacher equation editor applicationfurther includes one or more program instructions for transmitting alearning reinforcement signal to the student computer. The reinforcementsignal is transmitted at substantially the same time as the comparisonof the response with the one or more answers completes. The teacherequation editor application may include a web browser application.

The student equation editor application includes one or more programinstructions for receiving a question description via the communicationsnetwork, displaying the question description on the displaycorresponding to the student computer, and receiving one or moreresponses to the question description via the input device. Eachresponse includes one or more of an equation and an expression. Theinput device for the student computer includes a pointing device and/ora keyboard. At least one response is received in a character syntaxand/or a rendered format. The student equation editor applicationfurther includes one or more program instructions for transmitting atleast one response to the teacher computer via the communicationsnetwork. In an embodiment, transmitting at least one response occurs atsubstantially the same time as the at least one response is received viathe input device. The at least one response is transmitted in acharacter syntax. The student equation editor application furtherincludes one or more program instructions for generating at least onelearning reinforcement signal, and displaying the at least one learningreinforcement signal on the display corresponding to the studentcomputer display. Generating at least one reinforcement signal occurs atsubstantially the same time as at least one response to the questiondescription is received. The student equation editor application furtherincludes one or more program instructions for receiving at least onelearning reinforcement signal from the teacher computer via thecommunications network, and displaying the at least one learningreinforcement signal on the display corresponding to the studentcomputer. The student equation editor application includes a web browserapplication.

In an embodiment, the system for editing, comparing and resolvingequations further includes a comparison device. Each student computer,each teacher computer and the comparison device are operablyinterconnected via the communications network. The comparison deviceincludes a computer-readable storage medium. The comparison deviceincludes a comparison application comprising one or more programinstructions for receiving a response from one of the plurality ofstudent computers via the communications network, and comparing theresponse with the one or more answers corresponding to the questiondescription. At least one response may be received in a rendered formatand/or in a character syntax. In an embodiment, comparing the responseincludes rendering the response from the character syntax into arendered expression. In an embodiment, the teacher equation editorapplication further includes one or more programming instructions forreceiving the response, rendering the response into a renderedexpression, and displaying the rendered expression on the display of theteacher computer. The comparison application further includes one ormore program instructions for storing an indication that the response iscorrect, if the response is equal to at least one answer, and storing anindication that the response is incorrect, if the response is not equalto at least one answer. The comparison application further includes oneor more program instructions for transmitting a learning reinforcementsignal to the student computer. The reinforcement signal is transmittedat substantially the same time as the comparison of the response withthe one or more answers completes. The student equation editorapplication further includes one or more program instructions fortransmitting at least one response to the comparison device via thecommunications network. In an embodiment, transmitting at least oneresponse occurs at substantially the same time as the at least oneresponse is received via the input device. The at least one response istransmitted in a character syntax. The student equation editorapplication further includes one or more program instructions forreceiving at least one learning reinforcement signal from the comparisondevice via the communications network.

In an embodiment, a method of editing, comparing and resolving equationsincludes receiving a question description on a teacher computer system,receiving one or more answers on a teacher computer system, andtransmitting the question description to a plurality of student computersystems. Each answer includes one or more of an equation and anexpression. The method may further include receiving a plurality ofresponses, and determining, for each response, if the response matchesat least one answer. At least one response is received from each of theplurality of student computer systems. The method may further includetransmitting at least one learning reinforcement to the second computersystem associated with the response. The type of learning reinforcementmay be determined by whether the response matches at least one answer.

In an embodiment, a method of editing, comparing, and resolvingequations includes receiving a question description on a studentcomputer system from a teacher computer system, displaying the questiondescription, receiving at least one response to the questiondescription, and transmitting the at least one response to the teachercomputer system. Each response includes one or more of an equation andan expression. The method may further include receiving at least onelearning reinforcement from the teacher computer system.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and form a part ofthe specification, illustrate preferred embodiments of the presentinvention and, together with the description serve to explain theprinciples of the invention. The embodiments illustrated in the drawingsshould not be read to constitute limiting requirements, but instead areintended to assist the reader in understanding the invention.

FIG. 1 depicts a screen capture of an exemplary teacher equation editordialog window according to an embodiment of the present invention.

FIG. 2 depicts a screen capture of exemplary student responses on ateacher computer according to an embodiment of the present invention.

FIG. 3 depicts a screen capture of an exemplary teacher view of renderedstudent responses according to an embodiment of the present invention.

FIG. 4 depicts a screen capture of an exemplary student browser view ofa rendered equation and an equation editor according to an embodiment ofthe present invention.

FIG. 5 depicts a screen capture of a second exemplary student browserview of a rendered equation and an equation editor according to anembodiment of the present invention.

FIG. 6 depicts an exemplary embodiment of the present invention in whichthe comparison device is co-located with the teacher computer.

FIG. 7 depicts an exemplary embodiment of the present invention in whichthe comparison device is connected to the communications network.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In the following description, various embodiments of an equation editorsystem, along with methods of construction and use are provided. Theexamples contained herein refer specifically to mathematical equations.In general, the terms “mathematical equation” or simply “equation” referto technical expressions typically associated with mathematical and/orscientific symbols. However, it is to be understood that the inventionis not limited to the manipulation of mathematical equations orexpressions. Alternate embodiments of the present invention may be usedto represent, for example, sentence structure or chemical compounds.Additional embodiments of the invention may be utilized to manipulate avariety of symbols, expressions and the like.

In an embodiment, the present invention relates to on-line teaching andmonitoring of student learning on a plurality of computer devicesconnected via a communications network, such as an intranet and/or theInternet. Each computer may include an input device, a display and/or acomputer-readable storage medium for storing program instructions. Eachcomputer device may use, for example, a web browser as an interface withthe communications network. Preferably, the on-line teaching andlearning system provides change-by-change and/or real time reinforcementsignals for students. Simultaneously, the on-line teaching and learningsystem provides monitoring by the teacher of the current studentresponses and an indication of the correctness of the answer. The systemmay operate using a packet switched communications network, a cellswitched communications network, a direct connection or any othercommunications protocol or connection type. The system may include oneor more teacher computers. The student computers may be co-located withthe teacher computer and/or may connect to the teacher computer from aremote location.

A convenient interface for entering expressions and equations may beprovided. The interface may facilitate the submission of expressions andequations that would be difficult to enter using a standard keyboard. Ateacher may use an interface, such as the one shown in FIG. 1 at 100, topose one or more questions to students. Students may use a similarinterface, such as 405 in FIG. 4, to respond to questions. The teachercomputer, the student computer or a comparison device may evaluate thestudent responses on a change-by-change basis and/or in real time forcorrectness. In an embodiment, the teacher computer may further providereal time reinforcement signals to student computers. In an embodiment,each of the teacher computer and the student computers may generate realtime reinforcement signals. In an embodiment, student responses may beevaluated on a separate comparison device. The comparison device maygenerate and transmit real time reinforcement signals to one or more ofthe teacher computer and the student computer that transmitted thestudent response corresponding to the reinforcement signal. Simultaneousmonitoring, including updating each change in each student response, maybe provided by the teacher computer, the student computer and/or thecomparison device.

As shown in FIG. 2, a teacher computer may display an interface 200,which includes a question frame 205, an answer frame 210, and a currentstudent response frame 215. The question frame 205 may contain aquestion 207 that is transmitted to each of the student computers. Theanswer frame 210 may contain one or more answers 212 a-b to thecorresponding question 207. The current student response frame 215 mayinclude information pertaining to one or more student responses 217 a-c.In a preferred embodiment, for each student, the information pertainingto the one or more student responses 217 a-c may include, for example,the student's name 220, an answer correct field 222, the number of timesthe student has attempted to answer the question 224, and the currentstudent response 226. The current student response 226 may be updated ona change-by-change basis and/or in real time based on input from thecorresponding student using a student computer. The teacher interface200 may evaluate whether the current student response 226 for aparticular student is correct. If a current student response 226 matchesone or more of the answers 212 a-b, the teacher interface 200 mayprovide an indication in the corresponding answer correct field 222 andsend a reinforcement signal to the student computer.

A character-based syntax that describes the entered equation orexpression may be provided. The syntax may be designed to be easilyunderstood and entered by a student or teacher. In addition, therepresentation of the equation may allow easy verification ofcorrectness by a teacher using a teacher computer. A display showing therendered equation or expression may be provided, as shown in FIG. 3. Theteacher computer may render the equation or expression in real time asthe equation or expression is entered. Equations or expressions may beentered by, for example, selecting one or more symbols from a menu,selecting one or more symbols using buttons in the application, usingone or more hotkeys, and/or entering information in the character-basedsyntax. In an embodiment, all symbols, variables, and operations may bepresented to the user simultaneously as a palette of buttons. In thecase of question development, the rendered equation or expression may bedisplayed in the rendered expression display window 145 of the teacherequation editor interface 100. In the case of student responses,rendered equations or expressions 317 a-c based on equations orexpressions from one or more student computers may be displayed on theteacher computer in the teacher interface 200.

Preferably, teachers and students may use the equation editor to entermath notation, as required for questions, answers and student responses.In an Edit Math Notation dialog window, such as 100, text representationof math notation may be entered in a text box, such as 105. Other EditMath Notation dialog windows are shown at 410 and 505. The textrepresentation may be displayed substantially in real time on agraphical display. Text and/or select symbols and expressions may beselected from, for example, one or more toolbars, one or more menus, hotkeys, or a set of buttons. Selected entries may be highlighted in thetext box 105 by, for example, displaying the entries in a differentcolor, changing the background color for the entries, or altering thesize of the entries.

As shown in FIGS. 4 and 5, students are preferably provided with aquestion 406 within a frame 404 in an application on the studentcomputer. The question 406 may require the students to respond in theform of a response 415. A response 415 may be in the form of an equationor expression. Equations or expressions may be entered by, for example,selecting one or more symbols from a menu, selecting one or more symbolsusing buttons in the application, using one or more hotkeys, and/orentering information in the character-based syntax. In an embodiment,all symbols, variables, and operations may be presented to the usersimultaneously as a palette of buttons. The student computer maytransmit the response to the teacher computer or a separate comparisondevice where the response is automatically scored. The teacher mayoptionally subjectively evaluate a written explanation (not shown).

FIG. 6 depicts an exemplary embodiment of the present invention in whichthe comparison device is co-located with a teacher computer. In anembodiment, the teacher computer 605 may compare responses to a questiondescription received from the student computers 620 a-c to one or moreanswers corresponding to the question description using a comparisondevice 610 that is resident in the teacher computer 605. A response maybe transmitted from a student computer, such as 620 a, to the teachercomputer 605 via a communications network 615. Once the teacher computer605 receives a response, the comparison device 610 may compare theresponse with one or more answers and transmit a reinforcement signal tothe student computer 620 a via the communications network 615. Thenature of the reinforcement signal may be based on whether thecomparison device 610 favorably compares the received response to theone or more answers.

FIG. 7 depicts an exemplary embodiment of the present invention in whichthe comparison device is connected to the communications network. In analternate embodiment, the comparison device 610 may be connected to theteacher computer 605 via the communications network 615. One or moreanswers to a question description may be contained on a comparisondevice 610. In an embodiment, the teacher computer 605 may transmit theone or more answers to the comparison device 610. The teacher computer605 may then transmit the question description to the student computers620 a-c via the communications network 615. A response generated by astudent computer, such as 620 a, may be transmitted to the comparisondevice 610 via the communications network 615. The comparison device 610may transmit a reinforcement signal to the teacher computer 605 and/orthe student computer from which the response was received 620 a via thecommunications network 615. The nature of the reinforcement signal maybe based upon whether the comparison device 610 favorably compares theresponse to the one or more answers.

In an embodiment, a comparison device 610 may be resident on eachstudent computer 620 a-c. In this embodiment, a teacher computer 605 maytransmit a question description and one or more answers to each studentcomputer 620 a-c via the communications network 615. The studentcomputers may display the question description. The one or more answersmay be sent to the comparison device 610 and may not be displayed. As auser responds to the question description, the comparison device 610 maycompare the response to the one or more answers and may generate areinforcement signal. The nature of the reinforcement signal may bebased upon whether the comparison device 610 favorably compares theresponse to the one or more answers.

In an embodiment, an interface may implement at least one of thefollowing commands and functions. Examples showing the use of thecommands and functions according to the preferred embodiment arepresented for clarity where appropriate. Any standard computerinterface, such as toolbars, menus, buttons, hot keys and the like maybe used to implement the present invention. The scope of the presentinvention is not intended to be limited to the embodiment presentedbelow, which is presented only to further describe one of many possibleembodiments of the present invention.

Keyboard Entries

RETURN—Press the ENTER key to insert “RETURN” at the current insertionpoint in the text box. In response to pressing ENTER, the next notationmay be displayed below the previously entered notation.

TAB—Press the TAB key to move to and select the next insertion marker orto move to the end of the text entry in the text box.

Insertion Markers

As shown in FIG. 1, toolbar buttons for parentheses 110, fraction 115,square root 120, superscript 125, and subscript 130 may be presented inan equation editor dialog window 100. The buttons 110-130 may insertcharacters and special insertion markers associated with the respectivebutton. The cursor may blink in the text box 105 and a vertical gray bar(not shown) may be displayed when one of these buttons 110-130 isselected. An insertion marker acts as a placeholder for the content ofthe expression. For example, to enter “(x+y),” the parentheses button110 may be selected. The insertion marker may appear between the openand close parentheses. The user may then type “x+y” at the insertionpoint.

Button/Menu Entries

PARENTHESES—Parentheses may be entered directly into the text box 105.Alternatively, a parentheses button 110 or a parentheses menu item orhot key sequence may be selected to insert parentheses enclosing aninsertion marker. If text is selected prior to clicking the parenthesesbutton 110, selecting the parentheses menu item or entering theparenthesis hot key sequence, the selected text may be surrounded byparentheses.

FRACTION—A forward slash (“/”) may be entered directly into the text box105 to represent a fraction (e.g., type “x/y”), or the fraction button115 or a fraction menu item or hot key sequence may be selected toinsert a forward slash and parentheses enclosing insertion markers foreach of the numerator and the denominator. For example, to insert“(x+y)/(1+x),” a user may click the fraction button 115, select thefraction menu item or enter the fraction hot key sequence, type “x+y,”press TAB, and type “1+x.” If text is selected prior to clicking thefraction button 115, selecting the fraction menu item or entering thefraction hot key sequence, the selected text becomes the numerator ofthe fraction and is automatically enclosed in parentheses.

SQUARE ROOT—The square root button 120 or the square root menu item maybe selected, or the square root hot key sequence may be entered, toinsert “\SQRT” followed by parentheses enclosing an insertion marker.For example, to insert the notation for the square root of 4, a user mayclick the square root button 120, select the square root menu item orenter the square root hot key sequence and type “4.” If text is selectedprior to clicking the square root button 120, selecting the square rootmenu item or enter the square root hot key sequence, the selected textis surrounded by parentheses and becomes the content of the square rootexpression.

SUPERSCRIPT—The notation for a superscript includes two expressions: thesubject expression to which the superscript is attached and thesuperscript expression, which is displayed in a smaller font higher thanthe subject expression. The superscript button 125, the superscript menuitem or superscript hot key sequence may be selected to enter “\SUPER”followed by parentheses enclosing an insertion marker for thesuperscript expression. For example, to insert the notation forx-squared, a user may type “x,” click the superscript button 125, selectthe superscript menu item or enter the superscript hot key sequence, andtype “2.” If text is selected prior to selecting the superscript button125 or the superscript menu item, or entering the superscript hot keysequence, the selected text becomes the superscript and is automaticallyenclosed in parentheses.

SUBSCRIPT—The notation for subscript includes two expressions: thesubject expression to which the subscript is attached and the subscriptexpression, which is displayed in a smaller font lower than the subjectexpression. The subscript button 130, the subscript menu item or thesubscript hot key sequence may be selected to enter “\SUB” followed byparentheses enclosing an insertion marker for the subscript expression.For example, to insert the notation for x-squared, a user may type “x,”click the subscript button 130, select the subscript menu item or enterthe subscript hot key sequence, and type “2.” If text is selected priorto selecting the subscript button 130, selecting the subscript menu itemor entering the subscript hot key sequence, the selected text becomesthe subscript and is automatically enclosed in parentheses.

MATH SYMBOL—Four categories of symbols may be provided: Relationalsymbols 420, Operator symbols 425, Greek characters 430, andMiscellaneous/Other symbols 435. To access the symbols, a user may clickthe math symbol button 135, select the math symbol menu item or enterthe math symbol hot key sequence. A menu may be displayed in which eachof the four categories is represented. Upon selection of a category, asub-menu may then be displayed in which the symbols corresponding to theselected category are displayed. The user may select a desired symbol.The symbol may then be entered at the current insertion point in thetext box. FIG. 4 depicts a sub-menu 440 listing exemplary Relationalsymbols 420 according to an embodiment of the present invention. FIG. 5depicts a sub-menu 510 listing exemplary Operator symbols 425 accordingto an embodiment of the present invention.

Nesting Expressions

Expression may be nested to many levels of complexity. For example, toinsert a fraction inside a square root symbol, a user may click thesquare root button 120, click the fraction button 115, type thenumerator, press TAB and type the denominator. Alternatively, the usermay click the fraction button 115, type the numerator, press TAB, typethe denominator, select the fraction and click the square root button120. Alternatively, a user may select a menu item or enter a hot keysequence instead of selecting a button.

Editing Math Notation

Each entry from a toolbar button 110-130 may be treated as a single unitwhen the text representation is edited.

To edit a question that uses math notation, a user may select the mathnotation and click the MATH NOTATION button (not shown). The Edit MathNotation dialog box 100, such as the one depicted in FIG. 1, may then bedisplayed. The user may edit the math notation using the Edit MathNotation dialog box 100. Upon completion, the user may click an OKbutton 140.

In order to edit a math notation answer, a user may double-click insidethe answer. The Edit Math Notation dialog box 100 may then be displayed.The user may edit the math notation using the Edit Math Notation dialogbox 100 and click the OK button 140 upon completion.

Alternate Edit Math Notation dialog boxes may be implemented for ateacher computer and a student computer. The Edit Math Notation dialogbox 100 depicted in FIG. 1 may be used on a teacher computer and includea rendered expression display window 145 which may show how the enteredtext string will be displayed upon acceptance of the text string. Theexpression display window 145 may be used to verify the correctness ofthe text string entered in the teacher-accessible portion of the EditMath Notation dialog box 100. As shown in FIG. 4, an exemplary Edit MathNotation dialog box 410 for a student computer may be incorporated intoan Equation Editor application 402 implemented within a web browser 400.As shown in FIG. 5, an Edit Math Notation dialog box 505 for a studentcomputer may alternately be incorporated into a separate Equation Editorapplication 500.

Although the invention has been described with reference to thepreferred embodiments, it will be apparent to one skilled in the artthat variations and modifications are contemplated within the spirit andscope of the invention. The drawings and description of the preferredembodiments are made by way of example rather than to limit the scope ofthe invention, and it is intended to cover within the spirit and scopeof the invention all such changes and modifications.

What is claimed is:
 1. A system for editing, comparing, and resolvingequations, comprising: at least one teacher computer that implements ateacher equation editor application that generates a questiondescription and generates at least one answer corresponding to thequestion description and including at least one of an equation and anexpression; at least one student computer that implements a studentequation editor application that generates a response corresponding tothe question description and including at least one of a responseequation and a response expression; at least one comparison device thatcompares the response with the answer and outputs a comparison result;and a communications network operably connecting the teacher computer,the student computer, and the comparison device, wherein changes to theresponse received at the student equation editor application aretransmitted to the teacher computer and displayed using the teachercomputer on a change-by-change basis, wherein the changes to theresponse are received in rendered format, wherein the student equationeditor is configured to convert the rendered format to a charactersyntax in real time and to transmit the character syntax to the teachercomputer in real time, and wherein the teacher computer is configured totranslate the character syntax to a rendered format for display in realtime.
 2. The system of claim 1 wherein the teacher computer generatesthe question via manual operator input.
 3. The system of claim 1 whereinthe teacher computer generates the answer via manual operator input. 4.The system of claim 1 wherein the comparison device is the teachercomputer.
 5. The system of claim 1 wherein the comparison result istransmitted as a learning reinforcement signal to at least one of theteacher computer and the student computer.
 6. The system of claim 1wherein the student equation editor application comprises one or moreprogram instructions for: receiving the question description via thecommunications network; displaying the question description on a studentcomputer display; and receiving one or more responses to the questiondescription via a student computer input device.
 7. The system of claim6 wherein the student computer input device comprises a pointing device.8. The system of claim 6 wherein the student computer input devicecomprises a keyboard.
 9. The system of claim 6 wherein the studentequation editor application further comprises one or more programinstructions for: receiving one or more answers corresponding to thequestion description via the communications network; and comparing eachresponse with the one or more answers corresponding to the questiondescription.
 10. The system of claim 9 wherein the student equationeditor application further comprises one or more program instructionsfor: generating at least one learning reinforcement signal; anddisplaying the at least one learning reinforcement signal on the displaycorresponding to the student computer display.
 11. The system of claim10 wherein generating at least one reinforcement signal occurs atsubstantially the same time as at least one response to the questiondescription is received.
 12. The system of claim 6 wherein the studentequation editor application further comprises one or more programinstructions for: receiving at least one learning reinforcement signalfrom the teacher computer via the communications network; and displayingthe at least one learning reinforcement signal on the student computerdisplay.
 13. The system of claim 1 wherein the student equation editorapplication comprises a web browser application.
 14. The system of claim1, wherein the changes are displayed using the teacher computer in realtime.
 15. The system of claim 1, wherein the changes are displayed usingthe teacher computer each time a character of the response is changed atthe student equation editor application.
 16. A method for editing,comparing, and resolving equations, comprising: operably interconnectinga communications network, a teacher computer, a student computer, and acomparison device; implementing with the teacher computer a teacherequation editor application that generates a question description andgenerates at least one answer corresponding to the question descriptionand including at least one of an equation and an expression;implementing with the student computer a student equation editorapplication that generates a response corresponding to the questiondescription and including at least one of a response equation and aresponse expression; transmitting changes to the response received bythe student equation editor application to the teacher computer, whereinthe changes are displayed using the teacher computer on achange-by-change basis, wherein the changes to the response are receivedin rendered format, wherein the student equation editor is configured toconvert the rendered format to a character syntax in real time and totransmit the character syntax to the teacher computer in real time, andwherein the teacher computer is configured to translate the charactersyntax to a rendered format for display in real time; and using thecomparison device to compare the response with the answer and output acomparison result.
 17. The method of claim 16 further comprisinggenerating the question via manual operator input.
 18. The method ofclaim 16 further comprising generating the answer via manual operatorinput.
 19. The method of claim 16 further comprising transmitting thecomparison result as a learning reinforcement signal to at least one ofthe teacher computer and the student computer.
 20. The method of claim16 wherein the student equation editor application comprises one or moreprogram instructions for: receiving a question description via thecommunications network; displaying the question description on a studentcomputer display; and receiving one or more responses to the questiondescription via a student computer input device.
 21. The method of claim20 wherein the student computer input device comprises a pointingdevice.
 22. The method of claim 20 wherein the student computer inputdevice comprises a keyboard.
 23. The method of claim 20 wherein thestudent equation editor application further comprises one or moreprogram instructions for receiving at least one learning reinforcementsignal from the comparison device via the communications network. 24.The method of claim 16 wherein the student equation editor applicationcomprises a web browser application.
 25. The method of claim 16, whereinthe changes are displayed using the teacher computer in real time.
 26. Anon-transitory computer program product for editing, comparing, andresolving equations, comprising a computer-readable storage mediumcontaining program instructions tangibly embodied thereon as code meansfor: operably interconnecting a communications network, a teachercomputer, a student computer, and a comparison device; implementing withthe teacher computer a teacher equation editor application thatgenerates a question description and generates at least one answercorresponding to the question description and including at least one ofan equation and an expression; implementing with the student computer astudent equation editor application that generates a responsecorresponding to the question description and including at least one ofa response equation and a response expression; transmitting changes tothe response received by the student equation editor application to theteacher computer, wherein the changes are displayed using the teachercomputer on a change-by-change basis, wherein the changes to theresponse are received in rendered format, wherein the student equationeditor is configured to convert the rendered format to a charactersyntax in real time and to transmit the character syntax to the teachercomputer in real time, and wherein the teacher computer is configured totranslate the character syntax to a rendered format for display in realtime; and using the comparison device to compare the response with theanswer and output a comparison result.
 27. The computer program productof claim 26 further comprising code means for generating the questionvia manual operator input.
 28. The computer program product of claim 26further comprising code means for generating the answer via manualoperator input.
 29. The computer program product of claim 26 furthercomprising code means for transmitting the comparison result as alearning reinforcement signal to at least one of the teacher computerand the student computer.
 30. The computer program product of claim 26,wherein the changes are displayed using the teacher computer in realtime.
 31. A method of editing, comparing, and resolving equationscomprising: receiving a question description on a student computersystem from a teacher computer system; displaying the questiondescription; receiving at least one response to the questiondescription, wherein each response comprises one or more of an equationand an expression; and transmitting the at least one response to theteacher computer system, wherein received changes to the response aretransmitted to the teacher computer system and displayed using theteacher computer system on a change-by-change basis, wherein the changesto the response are received in rendered format, wherein the renderedformat is converted to a character syntax in real time and the charactersyntax is transmitted to the teacher computer in real time, and whereinthe teacher computer system is configured to translate the charactersyntax to a rendered format for display in real time.
 32. The method ofclaim 31, wherein the changes are displayed using the teacher computerin real time.
 33. The method of claim 31, further comprising: receivingat least one learning reinforcement signal from the teacher computersystem.